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Posted

unfortunately I mathematically challenged so I can't help you with the formula sort of. but I can give you a reference here is a manual for a timing machine that I do not have but I do have a collection of timing machine manuals and it has the formula.

B600_english -.pdf

Posted (edited)

Interesting, two equations for the same calculation. However π* has an asterisks.

• = optional

Sorry, I ponder as well but in this case I couldn't help myself 😁

Edited by Endeavor
Posted
1 hour ago, Endeavor said:

Interesting, two equations for the same calculation. However π* has an asterisks.

• = optional

Sorry, I ponder as well but in this case I couldn't help myself 😁

It’s a common thing in computer circles that * is used to denote multiplication 

 

Tom

Posted
1 hour ago, tomh207 said:

It’s a common thing in computer circles that * is used to denote multiplication 

 

Of course I know that, just giving it a twist 😉

 

  • Haha 1
Posted (edited)

I took a watch and measured the waveform on an oscilloscope to get ta.  In order to get the amplitude reported on the timegrapher, I have to divide by pi.  So, it needs to be there.

I have done the derivation where the rotation of the balance wheel is approximated as a sinusoid [sin(2 * pi * f * t)].  When the argument of a sin() is a small angle, it can be approximated as the angle itself:

sin(theta) ~ theta for small theta.

Thus, in the derivation, sin(2 * pi * f * t) becomes 2*pi*f*t.

So that is where pi enters the expression for Amplitude.

Edited by LittleWatchShop
Posted (edited)

BR = beat rate (e.g. 18000)
T = swing period (e.g. 0.4 s)
T = 2 * 3600 / BR
LA = lift angle (@ t1)
A = amplitude angle (@ T/2)
———————————

A = LA / sin( 2 * Pi * t1 / T)

here  sin(x) about equal to x:
A = (LA * T) / (2 * Pi * t1)
   = (LA * 3600) / (Pi * t1 * BR)
   = (LA * 1146) / (t1 * BR)

Frank

Edited by praezis
  • Like 2

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